AQA-Style Year 10 Foundation Paper 1

Question 1 [1 marks]

Indices and Standard Form

Write the number 45000 in standard form.

Question 2 [2 marks]

Angles and Geometrical Reasoning

Lines l and m are parallel and are crossed by a straight transversal. Angle y is in the corresponding position to the 118 degree angle marked above line l.

Question 3 [3 marks]

Graphs and Coordinates

Complete the table of values for y = x^3 - 1. x : -2 , -1 , 0 , 1 , 2 y : -9 , _ , _ , _ , 7

Question 4 [4 marks]

Fractions, Decimals and Percentages

(Non-calculator)

Work out 10% of 340.

Work out 25% of 60.

Work out 30% of 150.

Question 5 [1 marks]

Ratio and Proportion

The ratio of concrete to sand in a mixture is 3:11. Write the amount of sand as a fraction of the total amount of mixture.

Question 6 [1 marks]

Area, Volume and Measures

Two similar triangles have corresponding sides 6 cm and 9 cm. What is the scale factor from the triangle with side 6 cm to the triangle with side 9 cm? Give your answer as a fraction.

Question 7 [1 marks]

Linear Algebra

Make h the subject of the formula V = l × w × h.

Question 8 [1 marks]

Ratio and Proportion

A recipe uses 3 cups of flour to make 12 biscuits. Work out how many cups of flour are needed to make 4 biscuits.

Question 9 [1 marks]

Linear Algebra

Solve the equation 3x = 15. Show your working.

Find x.

Question 10 [1 marks]

Ratio and Proportion

Write the ratio of blue tiles to yellow tiles in simplest form. There are 9 blue tiles and 6 yellow tiles.

Question 11 [1 marks]

Indices and Standard Form

Four students each write the number 84000 in standard form. Amir writes 8.4 x 10^4 Ben writes 84 x 10^3 Chloe writes 0.84 x 10^5 Dev writes 8.4 x 10^3 Exactly one student has written the number correctly in standard form. Write down the name of that student.

Question 12 [1 marks]

Linear Algebra

a = 6. Work out the value of a^2.

Question 13 [1 marks]

Indices and Standard Form

Write 7.2 x 10^-4 as an ordinary number.

Question 14 [2 marks]

Linear Algebra

Solve 4 - x < 9 Show your working.

Question 15 [2 marks]

Number and Calculation

Find the HCF of 24 and 36.

Question 16 [2 marks]

Linear Algebra

Solve 7 - x = 2x + 1 Show your working.

Question 17 [2 marks]

Number and Calculation

Show that 41472 is divisible by 8.

Question 18 [2 marks]

Linear Algebra

Make x the subject of the formula: y = 5x + 4

Question 19 [2 marks]

Number and Calculation

Calculate 56 x 34.

Question 20 [2 marks]

Angles and Geometrical Reasoning

The exterior angle of a regular polygon is 9 degrees. Work out the number of sides of the polygon.

Question 21 [2 marks]

Linear Algebra

Solve (x - 9) / 5 = 4 Show your working.

Question 22 [2 marks]

Number and Calculation

Write 180 as a product of prime factors.

Question 23 [2 marks]

Linear Algebra

Expand and simplify (x - 5)(x + 9)

Question 24 [2 marks]

Number and Calculation

The Year 7 class has football training every 5 days and the Year 8 class every 7 days. If both classes have training on Monday, after how many days will they next have training on the same day?

Question 25 [2 marks]

Linear Algebra

Make x the subject of the formula: y = 6x - 13

Question 26 [2 marks]

Ratio and Proportion

Priya and Noah share 35 stickers in the ratio 3:4. How many stickers does Priya receive?

Question 27 [3 marks]

Graphs and Coordinates

Complete the table of values for y = x^3 - 4. x : -2 , -1 , 0 , 1 , 2 y : _ , -5 , _ , -3 , 4

Question 28 [2 marks]

Linear Algebra

Solve 7x - 4 = 3x + 20

Question 29 [5 marks]

Sequences

Here are the first four terms of a geometric sequence. 5, 15, 45, 135

Find the common ratio of the sequence.

Find the 6th term of the sequence.

Explain whether 3000 is a term of the sequence.

Question 30 [3 marks]

Ratio and Proportion

Ravi has £3.60 and his sister has 90p. Write the ratio of Ravi's money to his sister's money in its simplest form.

Question 31 [4 marks]

Sequences

Special sequences of numbers include square numbers and triangular numbers.

Write down the first five square numbers.

Write down the first five triangular numbers.

The nth triangular number is given by the formula n(n + 1) / 2. Use this formula to find the 12th triangular number.

Question 32 [4 marks]

Angles and Geometrical Reasoning

A model is built from 1 cm cubes. The plan is a 2 by 3 rectangle. The front elevation shows heights 2 and 1 across the width: left column height 2 cm, right column height 1 cm, for each of the 3 positions along the length. Work out the total number of 1 cm cubes used in the model.

Question 33 [3 marks]

Graphs and Coordinates

Priya walks from home to the bus stop, waits for the bus, then travels quickly by bus to college. Sketch a distance-time graph to show Priya's journey. Label your axes Time and Distance from home.

Question 34 [5 marks]

Sequences

A sequence of patterns is built from matchsticks. Pattern 1 is a single triangle. Each new pattern joins one more triangle onto the end of a strip, sharing one edge with the triangle before it. Pattern 1 (one triangle) uses 3 matchsticks. Pattern 2 (two triangles) uses 5 matchsticks. Pattern 3 (three triangles) uses 7 matchsticks.

Write down the number of matchsticks needed for Pattern 4.

Find an expression, in terms of n, for the number of matchsticks in Pattern n.

Zainab claims that Pattern 20 uses exactly 39 matchsticks. Show that Zainab is wrong, and find the correct number of matchsticks in Pattern 20.

Question 35 [6 marks]

Graphs and Coordinates

y = x^3 - 9x

Show that y = x^3 - 9x can be written as y = x(x - 3)(x + 3).

Hence write down the coordinates of the three points where the graph of y = x^3 - 9x crosses the x-axis.

Write down the coordinates of the point where the graph crosses the y-axis.